設 f:I⊆R→R 為凸函數(convex function) ，其中a,b ϵ I , a<b，則下列不等式恆成立 f((a+b)/2)≤1/(b-a) ∫_a^b▒f(x) dx ≤1/2 [f(a)+f(b)] (1.1) 此為廣為人知的Hadamard雙邊不等式。 本文試著就此Hadamard雙邊不等式(1.1)，建立一些推廣與更細緻的結果。 the following double inequality f((a+b)/2)≤1/(b-a) ∫_a^b▒f(x) dx≤1/2 [f(a)+f(b)] (1.1) holds for all convex function on [a, b] is known in the literature as Hermite-Hadamard (or Hadamard ) inequality. The main purpose of this paper is to establish some generalizations and refinements of the inequality (1.1).
